{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 257 30 "Boat on a River Helper Program" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 223 "There are some PHYSLETS elsewh ere on this website that animate a boat trying to cross a river. You \+ can change the velocities of the boat and the river, and pick an angle , and the animation will show you where you end up. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 252 "Here is a little rout ine to calculate what angle to aim the boat so that it will land at a \+ particular point, given: the distance across (d), the river velocity (vr), the boat velocity (vb), and the distance along the far bank tha t you want to reach. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 33 "How to use this Maple Worksheet :" }}{PARA 0 "" 0 "" {TEXT -1 357 "Change the numbers on the second line as you need, and t hen click with the mouse on the RESTART line, and press to exe cute each line sequentially. (If you change the number again, you nee d to \"re-execute\" each following line to react to those changes .. s o press down through the worksheet (notice that Maple skips ov er the comment lines!)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 78 "d := 3.5: vr:= 7: vb:=5: x_wanted := -8: # chang e these numbers as needed !" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "x:=d*(tan(theta)-(vr/vb)*sec(theta)):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 287 "theta_degrees := `if`(vb evalf (d*(tan(arcsin(vb/vr))-(vr/vb)*sec(arcsin(vb/vr)))), \+ \"not possible - see below for maximum upstream dis tance\", simplify((180/Pi)*fsolve(x=x_wanted,theta))),simplify((180/Pi )*fsolve(x=x_wanted,theta)));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 253 "Note : if your river velocity is greater than your boat velocity, you might not be able to get to a particular point. Use the line below t o find the maximum distance upstream that you can have for the given c onditions, and the angle to use to get that." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 215 "theta_critical := `if`(vb >= vr,\"not applicabl e\",evalf((180/Pi)*arcsin(vb/vr))); x_maximum_upstream := `if`(vb>=vr, \"any location is possible because vb>vr!\",evalf(d*(tan(arcsin(vb/vr) )-(vr/vb)*sec(arcsin(vb/vr)))));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 30 "Worksheet technical details : " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 815 " In the third line above, the general expression is g iven for the distance along the far river bank (with the angle as a va riable). If Vb>Vr, then we can get to any point on the far side of th e river (thus the last maple line should give that information). But, if VbVr , or if the x_wanted is possible .. the fourth line will solve for the correct angle (in degrees) to use to get to that location." }}} {EXCHG {PARA 0 "" 0 "" {TEXT 260 20 "Related worksheets :" }{TEXT -1 2 " " }{TEXT 259 11 "BOATONRIVER" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }